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Asymmetric oscillations in thermosolutal convection

Published online by Cambridge University Press:  26 April 2006

D. R. Moore ,
N. O. Weiss  and
J. M. Wilkins
D. R. Moore
Affiliation:
Department of Mathematics, Imperial College, London SW7 2BZ, UK
N. O. Weiss
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
J. M. Wilkins
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

Thermosolutal convection provides a testbed for applications of nonlinear dynamics to fluid motion. If the ratio of solutal to thermal diffusivity is small and the solutal Rayleigh number RS is large, instability sets in at a Hopf bifurcation as the thermal Rayleigh number RT is increased. For two-dimensional convection in a rectangular box the fundamental mode is a single roll with point symmetry about its axis. The symmetries of periodic and steady solutions form an eighth-order group with invariant subgroups that describe pure single-roll and multiroll solutions. A systematic numerical investigation reveals a rich variety of spatiotemporal behaviour in the regime where RS [Gt ] RT−RS > 0. Point symmetry is broken and there is a branch of spatially asymmetric periodic solutions. These mixed-mode oscillations lose their temporal symmetry in a subsequent bifurcation, followed eventually by a transition to chaos. The numerical experiments can be interpreted by relating the physical form of the solutions to an appropriate bifurcation structure.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 233 , December 1991 , pp. 561 - 585
Copyright
© 1991 Cambridge University Press

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